Insights into the photovoltaic properties of indium sulfide as an electron transport material in perovskite solar cells

According to recent reports, planar structure-based organometallic perovskite solar cells (OPSCs) have achieved remarkable power conversion efficiency (PCE), making them very competitive with the more traditional silicon photovoltaics. A complete understanding of OPSCs and their individual parts is still necessary for further enhancement in PCE. In this work, indium sulfide (In2S3)-based planar heterojunction OPSCs were proposed and simulated with the SCAPS (a Solar Cell Capacitance Simulator)-1D programme. Initially, OPSC performance was calibrated with the experimentally fabricated architecture (FTO/In2S3/MAPbI3/Spiro-OMeTAD/Au) to evaluate the optimum parameters of each layer. The numerical calculations showed a significant dependence of PCE on the thickness and defect density of the MAPbI3 absorber material. The results showed that as the perovskite layer thickness increased, the PCE improved gradually but subsequently reached a maximum at thicknesses greater than 500 nm. Moreover, parameters involving the series resistance as well as the shunt resistance were recognized to affect the performance of the OPSC. Most importantly, a champion PCE of over 20% was yielded under the optimistic simulation conditions. Overall, the OPSC performed better between 20 and 30 °C, and its efficiency rapidly decreases above that temperature.


Method and simulation
The numerical modeling of the devices enables us to understand the solar cell dynamics without the need for actual manufacturing. It also provides a high-level outline of the device's functionality. The one-dimensional SCAPS (version 3.3.07) was used in this simulation study. In 2000, researchers at the University of Gent in Belgium created this open-source program, which can be downloaded at any time 35 . The SCAPS software assists in the modeling of planar and graded PV structures up to seven components, with the additional functionality of calculating the band alignment graph, current-voltage (J-V) behavior, quantum efficiency (QE), recombination and generation currents, and other essential PV characteristics. SCAPS-1D relies primarily on the well-established Poisson's formula and the continuity laws for electrons and holes to perform its calculations [36][37][38][39] . SCAPS is very powerful software for performing solar cell and a description of the programme, and the algorithms it uses, is found in the literature 40,41 and in its user manual 42 .
where q is the charge, V is the potential, p(x) is the free hole concentration, n(x) is the free electron concentration, ε is the dielectric permittivity, N + D (x) is the donor density, N − A (x) is the acceptor density, p t (x) is the hole trap concentration, n t (x) is the trap concentration of an electron, J n is the current density of an electron, J p is the current density of a hole, G n is the electron generation rate, G p is the holes generation rate, R n is the recombination rate of electrons, R p is the recombination rate of holes.
Here, we simulated a typical n-i-p PV architecture with CH3NH3PbI3 perovskite as the photoactive film, compact In 2 S 3 as the ETM, and Spiro-OMeTAD organic film as the HTM, with fluorine-containing SnO 2 (FTO) and gold (Au) as the front and back electrodes, respectively. In Fig. 1a, we have a graphical diagram of the FTO/ In 2 S 3 /CH 3 NH 3 PbI 3 /Spiro-OMeTAD/Au device assembly. Tables 1 and 2 summarize the fundamental device parameters of several materials utilized in this analysis that were acquired from the theoretical and experimental literature. The work functions for the front and back electrodes were 4.4 eV and 5.2 eV, respectively. The SCAPS software calculated the absorption spectrum of each layer based on the optical merits of the materials and the geometry of the device.
The defects were used 0.6 eV above the valence band with a particular energy of 0.1 eV, taking into account the Gaussian energy distribution and the capture cross-section of carriers of 10 -15 cm 2 . The radiative recombination coefficient for perovskite was 2.3 × 10 -9 cm 3 /s, which was taken into consideration. The modeling analysis added imperfections at the HTM/perovskite and perovskite/ETM interfaces about 10 10 cm −2 . The conventional AM 1.5 G spectrum and a temperature of 300 K were used for the computations. Figure 1b displays the band structure diagram for the suggested n-i-p OPSC layout. At the conduction band interface of In 2 S 3 and CH 3 NH 3 PbI 3 , a potential barrier of 0.12 eV exists, which is a beneficial barrier for the better transport of electrons from perovskite to ETM, whereas at the junction of the valence band of perovskite and (2) Continuity equation for the hole:   www.nature.com/scientificreports/ HTM, holes have to contend with a large barrier of 0.13 eV. The J-V plot of the suggested cell architecture was analyzed after the appropriate layer parameters and operational conditions were determined (as covered in this section). Figure 1c displays the calculated J-V graph and its initial output parameters. We attained a power conversion efficiency (PCE) of 19.71%, which is close to the PCE of 18.83% that has been published experimentally 33 . A slight mismatch between the experimental and computed results is that in the present research, the FTO and Au layers were utilized as front and back electrodes, where the thickness of front and back contacts cannot be changed. In the experimental research, however, they were employed as layers with appropriate thicknesses.
Ethics approval and consent to participate. This article does not contain any studies with human participants or animals performed by the authors. We comply with the ethical standards. We provide our consent to take part.

Results and discussion
Increasing the device's efficiency is highly dependent on the thickness of the absorber layer. Nevertheless, using a very thick photoactive layer leads to a low charge carrier extraction rate and considerable losses owing to charge recombination; finding the right equilibrium between these two variations is crucial. Therefore, optimizing the light-absorbing thickness becomes essential for determining photocarrier production and spectrum response in photovoltaics 47 . The obtained J-V graphs are shown in Fig 48 . Furthermore, the poor recombination due to the thin perovskite creates a high V OC . Increasing the absorber perovskite's thickness also boosts the layer's ability to absorb light with longer wavelengths. As a result, more charge carriers are produced, which leads to a rise in the value of the J SC 49 . However, with higher absorbance, the recombination rate of photocarriers also increases since photocarriers have to cover a longer distance before approaching the corresponding electrodes. The increase in perovskite thickness raises the R s , which causes a decrease in FF. The improvement in efficiency is attributable to the steady rise in J SC . Our calculations suggest that the ideal value for the perovskite thickness should be 0.7 µm for the highest performance of MAPbI 3 -based single-cation OPSC. Therefore, optimizing the thickness of the perovskite layer is crucial for achieving the highest efficiency in a perovskite solar cell. By carefully balancing the absorption of light and the extraction of charge carriers, an optimal thickness can be found that maximizes the photocurrent and minimizes recombination, leading to the best performance of the device. Figure 2f illustrates the external QE (EQE) of devices with varying MAPbI 3 film thicknesses. The EQE of the device was clearly improved when the MAPbI 3 light harvester thickness was less than 0.7 µm, which indicates that the improvement in absorption was high. Nevertheless, the EQE of the device rose less when the thickness of MAPbI 3 was more than 0.7 µm, indicating that the rise in absorption was less significant. As the MAPbI 3 film thickness increased, it was better able to absorb light of longer wavelengths 50 . The profile of carrier generation rate is also obtained and reported in Fig. 3 to validate the higher penetration of generation rate in the absorber layer at higher thicknesses.
The number of defects in the photoactive MAPbI 3 has a significant impact on the output quality of perovskite solar cells. The V OC of the device may be optimized by controlling the generation-recombination rate of the photocarriers inside the perovskite. Shockley-Read-Hall (SRH) recombination may provide a more adequate explanation for the correlation between N T and OPSC performance 37,49 . The perovskite defect density in this analysis ranges from 2.45 × 10 14 to 2.45 × 10 16 cm −3 , and its impact on how well our computed work performs is investigated. Figure 4a displays J-V graphs that have been plotted with varying N T values. Results show that a minor decrease in J SC -from 24.241 to 23.582 mA/cm 2 and a major reduction in V OC -from 1.188 to 0.991 V-are found when the N T is increased from 2.45 × 10 14 to 2.45 × 10 16 cm −3 (Table 3). Since FF is dependent on V OC , there is a significant decrease in FF values (from 79.163 to 66.498%). The efficiency was dramatically reduced from 22.79 to 15.55% because of these decreases in J SC , V OC , and FF values. This suggests that a rise in the N T values leads to a greater number of imperfections, which in turn raises the recombination process, as shown in Fig. 5. The efficiency of OPSC is significantly affected by the amount of doping used. Doping can be categorized as either n-type or p-type, depending on the dopants used. Thus, improving OPSC efficiency relies on setting the appropriate value of N A . Doping concentration levels can be adjusted experimentally in many different ways 51 . Doping concentrations and defect density values, for example, can be experimentally modified by adding different dopants or adjusting their concentrations in the perovskite material. Experimentally changing doping ratios and minimizing defects may also be accomplished by adjusting the relative amounts of cesium (Cs), methylammonium iodide (MAI), formamidinium iodide (FAI), and lead iodide (PbI 2 ) 52 .  www.nature.com/scientificreports/ Furthermore, the N A of the perovskite was adjusted from 10 16 to 10 20 cm −3 , and the results are shown in Fig. 4b to help understand the impact of doping on the OPSC performance. According to our findings, the J-V characteristics are unchanged at low N A levels. Nevertheless, the inherent built-in electric field (V bi ) rises when N A surpasses 10 18 cm −3 . The performance of the cell is enhanced by an increase in V bi because it leads to improved separation of photocarriers. J SC was shown to decrease with increasing N A levels ( Table 4). Auger recombination might explain a decline in J SC value with rising N A . Auger recombination rises with increasing doping ratios, which lowers device efficiency 53,54 . Here, a further decline in J SC was shown if the N A was raised above 10 19 cm −3 . As a result, we decided to set the highest value for N A in the current simulation at 10 19 cm −3 .
The series resistance (R s ) has a major effect on the operation of the OPSC, particularly the FF and short circuit current (I SC ). When the resistance of a series circuit rises, FF drops. Therefore, for higher levels of R s , the I SC begins to decrease as well. Hence, a device's efficiency suffers when R s is quite high 55 . This led researchers   www.nature.com/scientificreports/ to examine how the PCE and FF of perovskite photoactive material changed with variations in R s . We evaluate the performance of the OPSC while changing the R s from 0 to 12 Ω cm 2 to examine the impact of R s on OPSC performance. The J-V profiles for various resistances are depicted in Fig. 6a. Our research shows that the photovoltaic has superior performance and a higher FF at lower R s (Fig. 6b-e). The efficiency of the devices deteriorates rapidly as the R s rises. These findings are consistent with those reported in other studies 36,56 . Shunt resistance (R sh ) is caused by the several pathways for charge recombination in the OPSC 57 . We simulate the device's operation, changing the R sh from 0 to 1000 Ω cm 2 , to examine the impact of R sh on OPSC performance. Changing R sh affects several different device characteristics, as seen in Fig. 6f,j. The performance of OPSC is found to improve as R sh rises. PCE = 19.15% and FF = 73.13% at 800 Ω cm 2 , and at 1000 Ω cm 2 we obtain PCE = 19.35% and FF = 73.8%, respectively. Therefore, we determine that an R sh of 800 Ω cm 2 is optimal. Figure 7a illustrates how altering the ambient temperature from 17 to 57 °C has an impact on the J-V plots of the OPSC device. It turns out that both V OC and FF suffer when the temperature goes up. However, there are not any noticeable changes at J SC . Efficiency gradually drops because both V OC and FF are impacted by rising temperatures. This investigation demonstrates that OPSC in an ambient environment gives better efficiency, which is over 25%; however, as the temperature rises, this efficiency gradually declines, as shown in Fig. 7b. An increase in temperature increases the recombination and reverse saturation currents, which further reduce the V OC and device performance. In addition, when the device is running at a higher temperature, the bandgap gets smaller, which may lead to more exciton recombination and less efficiency 58 . This observation may be extremely important when choosing OPSC in tropical areas.
Finally, the performance of the optimized OPSC was compared to that of an OPSC made of indium gallium zinc oxide (IGZO) as an ETM layer (see Fig. 8a). Recently, IGZO has been used as an ETM; it offers great promise because of its high µ e , environmental stability, low processing temperatures, and comparable electron affinity to perovskite 37,44,59 . As we can see in inset table of Fig. 8, In 2 S 3 -based device showed comparable photovoltaic parameters to the IGZO-based device. The findings from this study are expected to facilitate the manufacturing of high-efficiency perovskite solar cells in the near future. The energy level layout is constructed by incorporating an ETM, a MAPbI 3 absorbing layer, and Spiro-OMeTAD as HTM. This arrangement affects the valence/conduction band offset, which refers to the variation in the valence band between the HTM and the perovskite, as well as the conduction band between the ETM and the perovskite. The energy level offset at the ETM/MAPbI 3 and the MAPbI 3 /HTM interfaces greatly affects the solar cell's performance 36 . Figure 8b,c shows that quasi-Fermi levels F n and F p coexist with E C and E V in the OPSCs based on In 2 S 3 and IGZO layers. As shown, the In 2 S 3 -and IGZO-based structures showed a small conduction band offset (CBO) of 0.121 eV and 0.294 eV at ETM/MAPbI 3 interface, indicating that In 2 S 3 ETM provides better interface for electron transportation. However, IGZO film showed larger valence band offset at ETM/MAPbI 3 interface, which is significant for blocking the backflow of holes and suppressing the recombination rate in the OPSC.
Finally, we estimated The EQE spectra of In 2 S 3 and IGZO ETM-based OPSCs, as shown in Fig. 8d. The EQE could vary depending on the specific features of the semiconductors and the design of the cell. IGZO ETMbased OPSC has been proven to demonstrate relatively higher QE spectrum across the visible spectrum than In 2 S 3 ETM-based OPSC. This is because IGZO has a wide bandgap, which allows it to absorb a minimal amount of visible light while still effectively extracting electrons from the MAPbI 3 film. In general, it can be concluded that the utilization of both In2S3 and IGZO ETMs can effectively enhance the EQE of OPSCs. However, the selection of a suitable ETM is dependent upon the specific needs of the device and the preferred wavelength range for optimal performance.
We have provided insights into the relationship between the device's performance and the defects' density, which could be useful for optimizing the fabrication process and improving the device's performance. One possible approach to address this issue is to optimize the growth conditions during the fabrication process to minimize the defect density. For example, by carefully controlling the temperature, pressure, and some other important parameters of spin coating method during the growth process, it is possible to reduce the number of defects in the device. Interface passivation and anion/cation engineering can also be done to reduce the defect density. Additionally, post-growth processing techniques such as annealing could also reduce the density of defects in the material. In summary, we agree that the feasibility of tuning the property of the device at the fabrication or industrial level is an important consideration.

Conclusions
For the first time, the SCAPS-1D model has explored the potential of In 2 S 3 as an alternate ETM film in OPSCs in an effort to increase PV stability, boost efficiency, and reduce hysteresis behavior. Problems with imperfections and high temperatures are fundamental to the simulation analysis. Theoretically, In 2 S 3 can substitute TiO 2 as Table 4. PV device parameters of OPSCs with varying concentration of the shallow acceptor in CH 3 NH 3 PbI 3 .      www.nature.com/scientificreports/

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.